A spring of negligible mass has force constant k = 1800 N/m. Part A How far must

Question

A spring of negligible mass has force constant k = 1800 N/m.

Part A

How far must the spring be compressed for an amount 3.40 J of potential energy to be stored in it?

Express your answer using two significant figures.

Part B

You place the spring vertically with one end on the floor. You then drop a book of mass 1.40 kg onto it from a height of 0.900 m above the top of the spring. Find the maximum distance the spring will be compressed.

Take the free fall acceleration to be 9.80 m/s2 . Express your answer using two significant figures.

Please explain all the steps!! I need to be able to figure out similar problems and am very confused about how to do part B...

Explanation / Answer

Here,

spring constant, k =1800 N/m

part A)

let the spring must be compressed is x

as Potential energy = 0.5 * k * x^2

3.40 = 0.5 * 1800 * x^2

x = 0.0615 m

the spring must be compressed by 0.0615 m

part B)

let the maximum compression is x

Using conservation of energy

m * g * (x + h) = 0.5 * k * x^2

1.40 * 9.8 * (0.90 + x) = 0.5 * 1800 * x^2

solving for x

x = 0.125 m

the maximum compression in the spring is 0.125 m

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